Simple systems of nonlinear recursions whose evolution is rather easily ascertained

TL;DR

This paper demonstrates that solutions to specific nonlinear polynomial recursions can be determined with relative ease, revealing intriguing behaviors such as asymptotic periodicity in their integer-valued evolution over time.

Contribution

It introduces a class of nonlinear recurrence systems whose solutions are more accessible and exhibits notable asymptotic periodicity, advancing understanding of their dynamic behavior.

Findings

Solutions are more easily ascertained for certain nonlinear recursions.

Systems display interesting asymptotic periodicity.

Evolution in the integer time variable shows remarkable patterns.

Abstract

It is shown that the solutions of certain systems of nonlinear \"Orst-order recursions with polynomial right-hand sides may be rather easily ascertained, and display interesting evolutions in their ticking time variable (taking integer values): for instance a remarkable kind of asymptotic periodicity.